I will add another comment about models and logic.

If I throw a baseball straight up in the air, then it will fall straight down, and the position will be given by a parabola. And that parabola says that the ball will keep gaining speed as it falls, quickly breaking the speed of light, and every other possible limit.

But logic says that the ball will hit the ground first. That was the logical assumption before the model: We are at or near the surface of the Earth.

Here in Lithuania, we have experts who apply models without consideration for their underlying logic. They can predict how many cases there will be next week. And they can explain why their predictions were wrong. But are we kidding ourselves to think that's especially helpful? At best, those are just mathematical interpolations. They aren't giving flesh to the bones of the underlying logic.

Again, the logistic curve, as a model, supposes constant conditions, which is to say, a constant policy. But policy is not at all constant. So then we would have to speak of a family of logistic curves. And whose mind can compare two logistic curves? And what does that logistic curve say more than a bell curve - that it has a start, a middle, an end, and a width? The rest is just interpolation.

It seems much more relevant, simple and helpful to speak of a family of exponential rates. Ordinary people are familiar with interest rates. Each policy brings us down to a particular rate. We have a terrace of rates. If we weaken control, then the rate will go up. So we can only soften policy in ways that don't weaken control. That is my understanding and it will be interesting if I'm wrong but otherwise I think my conclusions stand.